1) Since position plotted as distance on the y axis and time on the x, the slopes of the position graphs would be rise/run > y/x > distance/time > meters/second > velocity. A positive slope means velocity was increasing and that the object was moving farther away from the sensor (in the positive direction). Zero (0) slope indicates that the object was not moving relative to the sensor since the position was not changing. A negative slope on the position graph means that the object was moving closer to the sensor, decreasing the space between them. When the line on the position graph crosses the x axis, that means that the position is negative relative to the starting position or origin. While this may be easier to imagine with a simple particle in space, unfortunately, the sensor that was used had no way of measuring an object going essentially through and behind it. Because the sensor could not measure bidirectionally and the origin was always calibrated at 0 meters relative to the sensor (ie right in front of it), the position graph never crossed the x axis. Also, moving behind the sensor was not attempted so even if the sensor could detect bidirectionally, it would not have had the opportunity to get a reading of negative position.
2) Since the slope of a velocity graph is acceleration, positive slopes indicated positive acceleration. This means that the object had to be moving away from the sensor at an increasing rate. Zero (0) slope on a velocity graph indicates no acceleration, meaning the object moves forward at its current rate of motion. Negative slope on a velocity graph indicates negative acceleration, meaning the object is still moving away from the sensor, but at a decreasing rate (slowing down). The preceding applies for when y is positive.
Lab 2 - Graph Matching
1) Since position plotted as distance on the y axis and time on the x, the slopes of the position graphs would be rise/run > y/x > distance/time > meters/second > velocity. A positive slope means velocity was increasing and that the object was moving farther away from the sensor (in the positive direction). Zero (0) slope indicates that the object was not moving relative to the sensor since the position was not changing. A negative slope on the position graph means that the object was moving closer to the sensor, decreasing the space between them. When the line on the position graph crosses the x axis, that means that the position is negative relative to the starting position or origin. While this may be easier to imagine with a simple particle in space, unfortunately, the sensor that was used had no way of measuring an object going essentially through and behind it. Because the sensor could not measure bidirectionally and the origin was always calibrated at 0 meters relative to the sensor (ie right in front of it), the position graph never crossed the x axis. Also, moving behind the sensor was not attempted so even if the sensor could detect bidirectionally, it would not have had the opportunity to get a reading of negative position.
2) Since the slope of a velocity graph is acceleration, positive slopes indicated positive acceleration. This means that the object had to be moving away from the sensor at an increasing rate. Zero (0) slope on a velocity graph indicates no acceleration, meaning the object moves forward at its current rate of motion. Negative slope on a velocity graph indicates negative acceleration, meaning the object is still moving away from the sensor, but at a decreasing rate (slowing down). The preceding applies for when y is positive.
When the line crosses the x axis, that means the velocity of the object has changed from positive (away from the sensor in the positive direction) to negative. Physically, this would mean that the object would be changing direction from moving away from the sensor to moving closer to the sensor. This did happen in the experiment when the object being tracked would move towards the sensor relative to the position they were in prior to the change in motion. When in the negative y values in the velocity graph, the object was moving towards the sensor at an increasing rate. Zero (0) slope in the negative y values indicated that the object was moving closer the sensor at a constant rate of change. Positive slope in the negative y values meant that the object was moving towards the sensor but at a decreasing rate.
©Kevin Trinh 2011